Problem 4 Consider the following function
f
defined for all
x
and
y
by
f(x,y)=2(1-a^(2))x^(2)y^(2)-3x^(2)-3y^(2)+2axy+4
where
a
is a constant in
-1,1
. (a) Show that for
a=+-1,f
has only one stationary point. (b) Classify the point found in (a). (c) Show that for all
ain[-1,1]
, if
(x,y)
is a stationary point, then
x^(2)=y^(2)
. (Hint: consider
{:xf_(x)^(')(x,y)-yf_(y)^(')(x,y).)

Question

Problem 4 Consider the following function

f

defined for all

x

and

y

by

f(x,y)=2(1-a^(2))x^(2)y^(2)-3x^(2)-3y^(2)+2axy+4

where

a

is a constant in

-1,1

. (a) Show that for

a=+-1,f

has only one stationary point. (b) Classify the point found in (a). (c) Show that for all

ain[-1,1]

, if

(x,y)

is a stationary point, then

x^(2)=y^(2)

. (Hint: consider

{:xf_(x)^(')(x,y)-yf_(y)^(')(x,y).)

Accepted Answer

Expert Answer to -  Problem 4 Consider the following function f defined for all x and y by f(x,y)=2(1-a^(2))x^(2)y^(2)-

Answer

Solution for -  Problem 4 Consider the following function f defined for all x and y by f(x,y)=2(1-a^(2))x^(2)y^(2)-

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This an additional answer to -  Problem 4 Consider the following function f defined for all x and y by f(x,y)=2(1-a^(2))x^(2)y^(2)-

(Solved): Problem 4 Consider the following function f defined for all x and y by f(x,y)=2(1-a^(2))x^(2)y^(2)- ...